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Trigonometry Identities - Sum/Difference to Identity (Degrees)

Level 1

This math topic focuses on the practice of trigonometric identities specifically dealing with sum and difference identities in degrees. Each problem presents a trigonometric expression and requires the completion of the corresponding sum/difference identity. Skills being exercised include manipulation and simplification of complex expressions involving tangent, sine, and cosine functions. The goal is to correctly identify and apply the appropriate trigonometric identities to rewrite the given expressions, improving the understanding and application of these fundamental concepts in trigonometry.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry Identities - Sum/Difference to Identity (Degrees) Worksheet

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Trigonometry Identities - Sum/Difference to Identity (Degrees)
1
A LaTex expression showing \text{tan}{(210 to the power of circle + 45 to the power of circle )}
Complete the sum/difference identity for this expression
a A LaTex expression showing =\frac{\text{tan}(210 to the power of circle ) + \text{tan}(45 to the power of circle )}{1-\text{tan}(210 to the power of circle )\text{tan}(45 to the power of circle ) }
b A LaTex expression showing =\frac{\text{cos}(210 to the power of circle ) + \text{sin}(45 to the power of circle )}{1-\text{tan}(210 to the power of circle )\text{tan}(45 to the power of circle ) }
2
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(210 to the power of circle - 225 to the power of circle )}
a A LaTex expression showing =\text{sin}{(210 to the power of circle )}\text{cos}{(225 to the power of circle )} + \text{cos} to the power of 2 {(210 to the power of circle )}
b A LaTex expression showing =\text{cos}{(210 to the power of circle )}\text{cos}{(225 to the power of circle )} + \text{sin}{(210 to the power of circle )}\text{sin}{(225 to the power of circle )}
3
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(330 to the power of circle - 150 to the power of circle )}
a A LaTex expression showing =\text{cos}{(330 to the power of circle )}\text{cos}{(150 to the power of circle )} + \text{sin}{(330 to the power of circle )}\text{sin}{(150 to the power of circle )}
b A LaTex expression showing =\text{sin}{(330 to the power of circle )}\text{cos}{(150 to the power of circle )} - \text{cos}{(330 to the power of circle )}\text{sin}{(150 to the power of circle )}
4
A LaTex expression showing \text{tan}{(135 to the power of circle + 30 to the power of circle )}
Complete the sum/difference identity for this expression
a A LaTex expression showing =\frac{\text{cos}(135 to the power of circle ) + \text{sin}(30 to the power of circle )}{1-\text{tan}(135 to the power of circle )\text{tan}(30 to the power of circle ) }
b A LaTex expression showing =\frac{\text{tan}(135 to the power of circle ) + \text{tan}(30 to the power of circle )}{1-\text{tan}(135 to the power of circle )\text{tan}(30 to the power of circle ) }
5
Complete the sum/difference identity for this expression
A LaTex expression showing \text{tan}{(60 to the power of circle - 150 to the power of circle )}
a A LaTex expression showing =\text{sin}{(60 to the power of circle )}\text{cos}{(150 to the power of circle )} - \text{cos}{(60 to the power of circle )}\text{sin}{(150 to the power of circle )}
b A LaTex expression showing =\frac{\text{tan}(60 to the power of circle ) - \text{tan}(150 to the power of circle )}{1+\text{tan}(60 to the power of circle )\text{tan}(150 to the power of circle ) }
6
Complete the sum/difference identity for this expression
A LaTex expression showing \text{tan}{(315 to the power of circle + 135 to the power of circle )}
a A LaTex expression showing =\frac{\text{tan}(315 to the power of circle ) + \text{tan}(135 to the power of circle )}{1-\text{tan}(315 to the power of circle )\text{tan}(135 to the power of circle ) }
b A LaTex expression showing =\frac{\text{tan}(315 to the power of circle ) + \text{tan}(135 to the power of circle )}{\text{tan} to the power of 2 (315 to the power of circle )\text{tan} to the power of 2 (135 to the power of circle ) }
7
Complete the sum/difference identity for this expression
A LaTex expression showing \text{cos}{(30 to the power of circle + 135 to the power of circle )}
a A LaTex expression showing =\text{sin}{(30 to the power of circle )}\text{sin}{(135 to the power of circle )} - \text{cos}{(30 to the power of circle )}\text{cos}{(135 to the power of circle )}
b A LaTex expression showing =\text{cos}{(30 to the power of circle )}\text{cos}{(135 to the power of circle )} - \text{sin}{(30 to the power of circle )}\text{sin}{(135 to the power of circle )}
8
A LaTex expression showing \text{tan}{(330 to the power of circle - 225 to the power of circle )}
Complete the sum/difference identity for this expression
a A LaTex expression showing =\frac{\text{cos}(330 to the power of circle ) + \text{sin}(225 to the power of circle )}{1-\text{tan}(330 to the power of circle )\text{tan}(225 to the power of circle ) }
b A LaTex expression showing =\frac{\text{tan}(330 to the power of circle ) - \text{tan}(225 to the power of circle )}{1+\text{tan}(330 to the power of circle )\text{tan}(225 to the power of circle ) }